| kruskal.test {stats} | R Documentation |
Kruskal-Wallis Rank Sum Test
Description
Performs a Kruskal-Wallis rank sum test.
Usage
kruskal.test(x, ...)
## Default S3 method:
kruskal.test(x, g, ...)
## S3 method for class 'formula'
kruskal.test(formula, data, subset, na.action, ...)
Arguments
x |
a numeric vector of data values, or a list of numeric data vectors. Non-numeric elements of a list will be coerced, with a warning. |
g |
a vector or factor object giving the group for the
corresponding elements of |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see
|
subset |
an optional vector specifying a subset of observations to be used. |
na.action |
a function which indicates what should happen when
the data contain |
... |
further arguments to be passed to or from methods. |
Details
kruskal.test performs a Kruskal-Wallis rank sum test of the
null that the location parameters of the distribution of x
are the same in each group (sample). The alternative is that they
differ in at least one.
If x is a list, its elements are taken as the samples to be
compared, and hence have to be numeric data vectors. In this case,
g is ignored, and one can simply use kruskal.test(x)
to perform the test. If the samples are not yet contained in a
list, use kruskal.test(list(x, ...)).
Otherwise, x must be a numeric data vector, and g must
be a vector or factor object of the same length as x giving
the group for the corresponding elements of x.
Value
A list with class "htest" containing the following components:
statistic |
the Kruskal-Wallis rank sum statistic. |
parameter |
the degrees of freedom of the approximate chi-squared distribution of the test statistic. |
p.value |
the p-value of the test. |
method |
the character string |
data.name |
a character string giving the names of the data. |
References
Hollander M, Wolfe DA (1973).
Nonparametric Statistical Methods.
John Wiley & Sons, New York.
ISBN 9780471406358.
Pages 115–120.
See Also
The Wilcoxon rank sum test (wilcox.test) as the special
case for two samples;
lm together with anova for performing
one-way location analysis under normality assumptions; with Student's
t test (t.test) as the special case for two samples.
wilcox_test in package
coin for exact, asymptotic and Monte Carlo
conditional p-values, including in the presence of ties.
Examples
## Hollander & Wolfe (1973), 116.
## Mucociliary efficiency from the rate of removal of dust in normal
## subjects, subjects with obstructive airway disease, and subjects
## with asbestosis.
x <- c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects
y <- c(3.8, 2.7, 4.0, 2.4) # with obstructive airway disease
z <- c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis
kruskal.test(list(x, y, z))
## Equivalently,
x <- c(x, y, z)
g <- factor(rep(1:3, c(5, 4, 5)),
labels = c("Normal subjects",
"Subjects with obstructive airway disease",
"Subjects with asbestosis"))
kruskal.test(x, g)
## Formula interface.
require(graphics)
boxplot(Ozone ~ Month, data = airquality)
kruskal.test(Ozone ~ Month, data = airquality)